Apparatus and method for image reconstruction and CT system

ABSTRACT

A method for image reconstruction using projection data obtained by an asymmetric detector includes dividing the projection data into Regions  1, 2, 3, 4 , and  5 . Region  1  is an asymmetric region having detecting channels but no detecting channels symmetrical about a central channel. Region  2  is a transition region having detecting channels and there are detecting channels symmetrical about the central channel. Region  3  is a symmetric region having detecting channels and there are detecting channels symmetrical about the central channel. Region  4  is a transition region having detecting channels and there are detecting channels symmetrical about the central channel. Region  5  is a truncated region where there is no detecting channel. The method includes performing a view angle weighting on projection data in each of the five regions, and reconstructing a tomographic image of an irradiated subject from the weighted projection data.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of Chinese Patent Application No.201010530606.8 filed Oct. 29, 2010, which is hereby incorporated byreference in its entirety.

BACKGROUND OF THE INVENTION

The embodiments described herein generally relate to the field of CTimage reconstruction, and in particular to an apparatus and method forimage reconstruction and CT system.

It is well-known that CT systems are having an increasing effect onmedical diagnosis, because they can clearly image various organs of apatient so as to enable the doctors to easily identify the diseasedregion and to take corresponding measures of treatment. The assistanceof CT systems in medical treatment has become a very important as wellas an essential part in modern medicine.

Typically, a CT system includes a tube and a detector. The tube is usedfor emitting X-rays, and the detector is used for receiving the X-raysemitted by the tube and converting them into electrical signals to formprojection data. Then, images of the irradiated subject (patient) arereconstructed according to the projection data.

The detector usually includes a symmetric detector and an asymmetricdetector. The symmetric detector refers to a detector in which thenumbers of detecting units at both sides of the central channel (achannel corresponding to the center of rotation) of the detector areequal or are different by no more than two channels. The asymmetricdetector refers to a detector in which the numbers of detecting units atboth sides of the central channel of the detector are unequal and aredifferent by more than two channels.

The advent of the asymmetric detector in a CT system can either reducethe number of detecting units at one side of the central channel of thedetector so as to reduce the cost, or increase the number of detectingunits at one side of the central channel so as to enlarge the scan focusof view.

Compared to the symmetric detector, the projection data obtained byusing the asymmetric detector have data loss at one side of the centralchannel, so the reconstruction method used for the projection dataobtained by the symmetric detector is not applicable to the projectiondata obtained by the asymmetric detector. The reconstruction method forthe projection data obtained by the asymmetric detector has, therefore,become one of the hotspots that are studied in the industry.

An article titled “X-ray micro-CT with a displaced detector array” by GEWANG published in Medical Physics, 29 (7): 1634-6 in June 2002 describesa method of reconstruction under an asymmetric detector in an axialscan. However, the reconstructed image cannot have an image qualitysimilar to the original one in the central symmetric region under theasymmetric detector.

U.S. Pat. No. 6,873,676 and U.S. Pat. No. 6,452,996 disclose“convolution reconstruction algorithm for multi-slice CT” and “methodsand apparatus utilizing generalized helical interpolation algorithm”.These patents describe the convolution reconstruction algorithm/thegeneralized helical interpolation algorithm, which can better suppressnoises and image artifacts as compared to other two-dimensional helicalreconstruction algorithms, especially for the multi-row CT having morethan four rows.

U.S. Pat. No. 7,062,009 describes dividing the projection data into asymmetric region and an asymmetric region. For projection data in thesymmetric region, the helical interpolation weight adopts thecomplementary interpolation weight, while for the projection data in theasymmetric region, the helical interpolation weight adopts the directinterpolation weight. This patent describes the reconstruction method ofa helical scan under the asymmetric detector in general terms, but thereconstructed image has a quality defect. Moreover, this patent fails toprovide a solution to image reconstruction for multi-row CT having morethan four rows.

SUMMARY OF THE INVENTION

The main technical problem to be solved by the embodiments describedherein is to provide an apparatus and method for image reconstructionthat can make the quality of the image reconstructed from projectiondata obtained by the asymmetric detector to be the same as the qualityof the image reconstructed from projection data obtained by thesymmetric detector as well as a CT system.

According to one aspect, a method for image reconstruction is provided,which is used for image reconstruction according to projection dataobtained by the asymmetric detector. The method includes dividingprojection data into five regions: Region 1, Region 2, Region 3, Region4 and Region 5. Region 1 is an asymmetric region where there aredetecting channels but no detecting channels symmetrical about thecentral channel. Region 2 is a transition region where there aredetecting channels, and there are also detecting channels symmetricalabout the central channel. Region 3 is a symmetric region where thereare detecting channels and there are also detecting channels symmetricalabout the central channel. Region 4 is a transition region where thereare detecting channels and there are also detecting channels symmetricalabout the central channel. Region 5 is a truncated region where thereare no detecting channels. The method further includes performing a viewangle weighting on projection data in each of the five regions, andreconstructing the tomographic image of the irradiated subject fromweighted projection data.

For the axial scan, the weights of projection data in the five regionsare as follows: the weights of projection data in Region 1 are 1; theweights of projection data in Region 3 are ½; the weights of projectiondata in Region 5 are 0; the weights of projection data in the Region 2are 1˜½; and the weights of projection data in Region 4 are ½˜0.

The weights of projection data in Region 2 are obtained from thefollowing formula:

${{w(\gamma)} = {1 - {\frac{1}{2}*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}},$wherein w(γ) represents the weight of projection data obtained when thefan angle is γ; γ₀ represents the largest fan angle at the small fanangle side; Δγ represents the width of the transition region;

${{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )},$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function, and when its independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

The weights of projection data in 4 are obtained from the followingformula:

${w(\gamma)} = {\frac{1}{2} - {\frac{1}{2}*{{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}.}}}$

For the helical scan, the weights of projection data in the five regionsare as follows: the weights of projection data in Region 5 are 0; andthe weights of projection data in the remaining four regions are:

${\xi( {\gamma,\beta,i} )} = {\sum\limits_{n = 0}^{N - k}{{\alpha(n)}{w_{n}( {\gamma,\beta,i} )}}}$wherein, ξ(γ,β,i) represents the weight of projection data at theposition of fan angle γ in the i^(th) row of the asymmetric detectorunder the view angle β; N represents the number of rows of theasymmetric detector, k represents consecutive k rows in the asymmetricdetector and k=p, p represents the pitch, a(n) represents the weight ofsubset n and Σa(n)=1, and w_(n)(γ,β,i) represents, in subset n, theweight of projection data at the position of fan angle γ in the i^(th)row of the asymmetric detector under the view angle β.

For Region 3 and Region 1:

${w_{n}( {\gamma,\beta,i} )} = \{ \begin{matrix}{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {\beta - {\theta_{n,{m -}}( {\gamma,\beta,i} )}} )}{{\theta_{n,m}( {\gamma,\beta,i} )} - {\theta_{n,{m -}}( {\gamma,\beta,i} )}}},} & {{\theta_{n,{m -}}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,m}( {\gamma,\beta,i} )}} \\{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {{\theta_{n,{m +}}( {\gamma,\beta,i} )} - \beta} )}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} - {\theta_{n,m}( {\gamma,\beta,i} )}}},} & {{\theta_{n,m}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,{m +}}( {\gamma,\beta,i} )}} \\{0,} & {{otherwise},}\end{matrix} $wherein, λ_(n,m) represents the weight in the n^(th) subset with them^(th) kind of interpolation; θ_(n.m)(γ,β,i) represents the center ofview angle when calculating the weight w_(n)(γ,β,i) in the n^(th) subsetunder the m^(th) kind of interpolation, and the weight thereof is 1;θ_(n,m−)(γ,β,i) represents the lower boundary of the view angle whencalculating w_(n)(γ,β,i) under the m^(th) kind of interpolation, and theweight there of is 0; and θ_(n.m+)(γ,β,i) represents the upper boundaryof the view angle when calculating w_(n)(γ,β,i) under the m^(th) kind ofinterpolation, and the weight there of is 0.

For 3:

${{\theta_{{n.m} -}( {\gamma,\beta,i} )} = {\phi_{i,m} - \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{{n.m} +}( {\gamma,\beta,i} )} = {\phi_{i,m} + \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n.m}( {\gamma,\beta,i} )} = {\phi_{i,m} - {\delta_{m}*\gamma}}}$wherein,

${\phi_{i,m} = \frac{2i\;\pi}{p}},$φ_(i,m) represents the center of a view angle of the central channel inthe i^(th) row; and δ_(m) is the inclined slop of the m^(th) kind ofinterpolation.

For Region 1:

θ_(n.m)(γ, β, i) = θ_(n, m)(−γ₀ + Δ γ, β, i) = ϕ_(i, m) − δ_(m) * (−γ₀ + Δ γ)$\begin{matrix}{{\theta_{{n.m} -}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} - \frac{2\;\pi}{p}}} \\{{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} - \frac{2\;\pi}{p}}},}\end{matrix}$ $\begin{matrix}{{\theta_{{n.m} +}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} + \frac{2\;\pi}{p}}} \\{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} + \frac{2\;\pi}{p}}}\end{matrix}$wherein γ₀ represents the largest fan angle at the small fan angle side;and Δγ represents the width of the transition region.

For Region 2:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{- \gamma_{0}},\beta,i} )} + {( {{w_{n}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} - {w_{n}( {{- \gamma_{0}},\beta,i} )}} )*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}$wherein,

${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function and when its independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

For Region 4:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{\gamma_{0} - {\Delta\;\gamma}},{\beta + {2*( {\gamma - \gamma_{0} + {\Delta\;\gamma}} )}},i} )}*{( {1 - {{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}} ).}}$

According to another aspect, an apparatus for image reconstruction isprovided, which is used for image reconstruction according to projectiondata obtained by the asymmetric detector. The apparatus includes aregion dividing unit for dividing projection data into five regions:Region 1, Region 2, Region 3, Region 4 and Region 5. Region 1 is anasymmetric region where there are detecting channels but no detectingchannels symmetrical about the central channel. Region 2 is a transitionregion where there are detecting channels and there are also detectingchannels symmetrical about the central channel. Region 3 is a symmetricregion where there are detecting channels and there are also detectingchannels symmetrical about the central channel. Region 4 is a transitionregion where there are detecting channels and there are also detectingchannels symmetrical about the central channel. Region 5 is a truncatedregion where there are no detecting channels. The apparatus furtherincludes a view angle weighting unit for performing a view angleweighting on projection data in each of the five regions; and areconstructing unit for reconstructing the tomographic image of theirradiated subject from weighted projection data:

For the axial scan, the weights of projection data in the five regionsare as follows: the weights of projection data in Region 1 are 1; theweights of projection data in Region 3 are ½; the weights of projectiondata in Region 5 are 0; the weights of projection data in Region 2 are1˜½; and the weights of projection data in Region 4 are ½˜0.

The weights of projection data in Region 2 are obtained from thefollowing formula:

${w(\gamma)} = {1 - {\frac{1}{2}*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}$wherein, w(γ) represents the weight of projection data obtained when thefan angle is γ; γ₀ represents the largest fan angle at the small fanangle side; Δγ represents the width of the transition region; and

${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function, and when its independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

The weights of projection data in Region 4 are obtained from thefollowing formula:

${w(\gamma)} = {\frac{1}{2} - {\frac{1}{2}*{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}$${trans}( {\gamma,{\gamma_{0} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )$is the transition function. Suppose Δγ=b and

${{\gamma_{0} - \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function, and when its independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

For the helical scan, the weights of projection data in the five regionsare as follows: the weights of projection data in Region 5 are 0; andthe weights of projection data in the remaining four regions are:

${\xi( {\gamma,\beta,i} )} = {\sum\limits_{n = 0}^{N - k}{{\alpha(n)}{w_{n}( {\gamma,\beta,i} )}}}$wherein, ξ(γ,β,i) represents the weight of projection data at theposition of a fan angle γ in the i^(th) row of the asymmetric detectorunder the view angle β;N represents the number of rows of the asymmetric detector, k representsconsecutive k rows in the asymmetric detector and k=p, p represents thepitch, a(n) represents the weight of subset n and Σa(n)=1, w_(n)(γ,β,i)represents, in subset n, the weight of projection data at the positionof fan angle γ in the i^(th) row of the asymmetric detector under theview angle β.

For Region 3 and Region 1:

${w_{n}( {\gamma,\beta,i} )} = \{ \begin{matrix}{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {\beta - {\theta_{n,{m -}}( {\gamma,\beta,i} )}} )}{{\theta_{n,m}( {\gamma,\beta,i} )} - {\theta_{n,{m -}}( {\gamma,\beta,i} )}}},} & {{\theta_{n,{m -}}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,m}( {\gamma,\beta,i} )}} \\{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {{\theta_{n,{m +}}( {\gamma,\beta,i} )} - \beta} )}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} - {\theta_{n,m}( {\gamma,\beta,i} )}}},} & {{\theta_{n,m}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,{m +}}( {\gamma,\beta,i} )}} \\{0,} & {{otherwise},}\end{matrix} $wherein, λ_(n,m) represents the weight in the n^(th) subset with them^(th) kind of interpolation; θ_(n.m)(γ,β,i) represents the center ofview angle when calculating the weight w_(n)(γ,β,i) in the n^(th) subsetunder the m^(th) kind of interpolation, and the weight thereof is 1;θ_(n,m−)(γ,β,i) represents the lower boundary of the view angle whencalculating (γ,β,i) under the m^(th) kind of interpolation, and theweight there of is 0; and θ_(n.m+)(γ,β,i) represents the upper boundaryof the view angle when calculating w_(n)(γ,β,i) under the m^(th) kind ofinterpolation, and the weight thereof is 0.

For Region 3:

${{\theta_{{n.m} -}( {\gamma,\beta,i} )} = {\phi_{i,m} - \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{{n.m} +}( {\gamma,\beta,i} )} = {\phi_{i,m} + \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n.m}( {\gamma,\beta,i} )} = {\phi_{i,m} - {\delta_{m}*\gamma}}}$wherein,

${\phi_{i,m} = \frac{2i\;\pi}{p}},$φ_(i,m) represents the center of view angle of the central channel inthe i^(th) row; and δ_(m) is the inclined slop of the m^(th) kind ofinterpolation.

For Region 1:

θ_(n.m)(γ, β, i) = θ_(n, m)(−γ₀ + Δ γ, β, i) = ϕ_(i, m) − δ_(m) * (−γ₀ + Δ γ)$\begin{matrix}{{\theta_{{n.m} -}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} - \frac{2\;\pi}{p}}} \\{{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} - \frac{2\;\pi}{p}}},}\end{matrix}$ $\begin{matrix}{{\theta_{{n.m} +}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} + \frac{2\;\pi}{p}}} \\{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} + \frac{2\;\pi}{p}}}\end{matrix}$wherein γ₀ represents the largest fan angle at the small fan angle side;and Δγ represents the width of the transition region.

For Region 2:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{- \gamma_{0}},\beta,i} )} + {( {{w_{n}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} - {w_{n}( {{- \gamma_{0}},\beta,i} )}} )*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}$wherein,

${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function and when its independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

For Region 4:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{\gamma_{0} - {\Delta\;\gamma}},{\beta + {2*( {\gamma - \gamma_{0} + {\Delta\;\gamma}} )}},i} )}*{( {1 - {{trans}( {\gamma,{\gamma_{0} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}} ).}}$

According to yet another aspect, a CT system is provided, which includesthe apparatus for image reconstruction described above.

Compared to the prior art, the apparatus and method for imagereconstruction and the CT system have the following advantageouseffects.

First, the embodiments described herein divide projection data into fiveregions and perform a view angle weighting on projection data in eachregion, so that the quality of the image reconstructed from projectiondata obtained by the asymmetric detector is the same as the quality ofthe image reconstructed from projection data obtained by the symmetricdetector.

Second, for the axial scan, the embodiments described herein employ thesame way of weighting as that adopted by the symmetric detector in mostof the regions of the central symmetric portion, so that the quality ofthe image reconstructed from the central regions is substantially thesame as the quality of image when using a symmetrical detector.

Third, for the helical scan, the embodiments described hereinincorporate the convolution reconstruction algorithm/generalized helicalinterpolation algorithm, so that most of the central symmetric portionshave better noise characteristics, and the span of a single slicereconstructed region is reduced in the axial direction to the greatestextent, especially for a multi-row CT having more than four rows.

Finally, the embodiments described herein perform view angle weightinginstead of projection data restoration, so the reconstruction time isbasically not increased.

BRIEF DESCRIPTION OF THE DRAWINGS

To a more thorough understanding of the disclosure of the presentinvention, reference is below made to the descriptions taken inconjunction with the drawings, wherein,

FIG. 1 illustrates a flow chart of an exemplary method for imagereconstruction;

FIG. 2 illustrates a schematic diagram of division of the five regionsof projection data;

FIG. 3 illustrates a schematic diagram of the weights of the asymmetricreconstruction in an axial scan;

FIG. 4 illustrates a schematic diagram of the result of thereconstruction in an axial scan;

FIG. 5 illustrates a schematic diagram of the convolution reconstructionalgorithm/generalized helical interpolation algorithm;

FIG. 6 illustrates a schematic diagram of the axial positions of theasymmetric reconstruction regions in a helical scan;

FIG. 7 illustrates a schematic diagram of the weights of the asymmetricreconstruction in a helical scan;

FIG. 8 illustrates a schematic diagram of the result of reconstructionin a helical scan.

DETAILED DESCRIPTION OF THE INVENTION

The specific embodiments of the present invention will be described indetail below, but the present invention is not limited to said specificembodiments.

According to one aspect, a method for image reconstruction is disclosed,which is used for image reconstruction according to the projection dataobtained by the asymmetric detector. As shown in FIG. 1, method includesdividing projection data into five regions: Region 1, Region 2, Region3, Region 4 and Region 5. Region 1 is an asymmetric region where thereare detecting channels but no detecting channels symmetrical about thecentral channel. Region 2 is a transition region where there aredetecting channels, and there are also detecting channels symmetricalabout the central channel. Region 3 is a symmetric region where thereare detecting channels, and there are also detecting channelssymmetrical about the central channel. Region 4 is a transition regionwhere there are detecting channels, and there are also detectingchannels symmetrical about the central channel. Region 5 is a truncatedregion where there is no detecting channel. The method further includesperforming the view angle weighting on projection data in each of thefive regions, and reconstructing the tomographic image of the irradiatedsubject from weighted projection data.

It can be seen from the above that the method for image reconstructionis to divide projection data into five regions (as shown in FIG. 2),perform a view angle weighting for each of the regions, and thenreconstruct the tomographic image of the irradiated subject fromweighted projection data, so that the quality of the image reconstructedfrom projection data obtained by the asymmetric detector is the same asthe quality of the image reconstructed from projection data obtained bythe symmetric detector.

As shown in FIG. 2, γ_(m) is the largest fan angle of the system (i.e.the largest fan angle at the large fan angle side), γ₀ is the largestfan angle at the small fan angle side, and Δγ is the width of thetransition region. In FIG. 2, the range of Region 1 is −γ_(m)≦γ≦−γ₀; therange of Region 2 is −γ₀<γ<−γ₀+Δγ; the range of Region 3 is−γ₀+Δγ≦γ≦γ₀−Δγ; the range of Region 4 is γ₀−Δγ<γ<γ₀; and the range ofRegion 5 is γ₀≦γ≦γ_(m).

The width of the transition region is generally not less than 20channels.

In terms of the way of scanning the subject, there are axial scans andhelical scans. The axial scan means that the table of the CT system doesnot move axially when scanning to obtain a CT tomography. The helicalscan means that the table of the CT system moves axially with uniformspeed when scanning to obtain a CT tomography.

For the axial scan, the weights of projection data in the five regionsare as follows: the weights of projection data in Region 1 are 1; theweights of projection data in Region 3 are ½; the weights of projectiondata in Region 5 are 0; the weights of projection data in Region 2 are1˜½; and the weights of projection data in Region 4 are ½˜0.

The weights of projection data in Region 2 can be obtained from thefollowing formula:

${w(\gamma)} = {1 - {\frac{1}{2}*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}$wherein w(γ) represents the weight of projection data obtained when thefan angle is γ; and

${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{{trans}( {\gamma,a,b} )} = {f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )}},{{{and}\mspace{14mu}{f(x)}} = {{3*x^{2}} - {2*{x^{3}.}}}}$

This is merely an example of the transition function. As for thedefinition of ƒ(x), in addition to ƒ(x)=3*x²−2*x³, any differentiablefunction is applicable as long as the function value of thedifferentiable function varies from 0 to 1 when its independent variablevaries from 0 to 1 and ƒ(x)+ƒ(1−x)=1 is satisfied.

When the axial scan is employed, the weights of projection data inRegion 4 can be obtained from the following formula:

${w(\gamma)} = {\frac{1}{2} - {\frac{1}{2}*{{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}.}}}$Suppose Δγ=b and

${{\gamma_{0} - \frac{\Delta\gamma}{2}} = a},$then,

${{{trans}( {\gamma,a,b} )} = {f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )}},{{{and}\mspace{14mu}{f(x)}} = {{3*x^{2}} - {2*x^{3}}}}$${wherein}\mspace{14mu}{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}$is a transition function.

This is merely an example of the transition function. As for thedefinition of ƒ(x), in addition to ƒ(x)=3*x²−2*x³, any differentiablefunction is applicable as long as the function value of thedifferentiable function varies from 0 to 1 when its independent variablevaries from 0 to 1 and ƒ(x)+ƒ(1−x)=1 is satisfied.

The process of performing image reconstruction using the method forimage reconstruction described herein under an axial scan is describedbelow through a specific example.

For example, one side of the asymmetric detector used has 444 channels,and the other side thereof has 300 channels, so the two sides areasymmetrical. The projection data obtained through the asymmetricdetector are divided into five regions using the axial scan, as shown inFIG. 2. In this example, γ_(m) is 27.4 degrees, γ₀ is 18.5 degrees, andΔγ is 6.2 degrees. Then, the view angle weighting is performed onprojection data in each of the five regions according to theabove-mentioned formula, and the weights of the 888 channels at 984 viewangles are calculated, as shown in FIG. 3. Finally, the tomographicimage of the irradiated subject is reconstructed according to theweighted projection data. Reconstruction of the tomographic image of theirradiated subject according to the weighted projection data can beperformed in any way known to those skilled in the art, and since it isthe existing technique, no detailed description will be given here.

As shown in FIG. 3, the weights of the 888 channels at 984 view anglesare in the left side, the weights of the 888 channels at one of the viewangles are in the right side. The weight of each channel is independentof the view angle, so for any view angle, the obtained correspondingrelationship between the weights and the channel remains the same.

As shown in FIG. 4, the leftmost part is the image reconstructed by thesymmetric detector, the middle part is the image reconstructed by theasymmetric detector using the method for image reconstruction describedherein, and the rightmost part is the image of the difference image ofthe two images. The left two images have a window width of 200 and awindow level of 60; and the rightmost image has a window width of 40 anda window level of 0. The centers of all images are in the center ofscan.

As can be seen from FIG. 4, the image (the middle image) reconstructedby the method for image reconstruction described herein has almost thesame quality in the central region as the image reconstructed by thesymmetric detector.

The above describes the method of reconstructing the tomographic imageof the irradiated subject through the projection obtained by theasymmetric detector with an axial scan. Next, the circumstances in ahelical scan will be described.

For the helical scan, the weights of the projection data in the fiveregions are as follows: the weights of the projection data in Region 5are 0 and the weights of the projection data in the remaining fourregions are:

${\xi( {\gamma,\beta,i} )} = {\sum\limits_{n = 0}^{N - k}{{\alpha(n)}{w_{n}( {\gamma,\beta,i} )}}}$wherein, ξ(γ,β,i) represents the weight of the projection data at theposition of fan angle γ in the i^(th) row of the asymmetric detectorunder the view angle β;N represents the number of rows of the asymmetric detector, k representsconsecutive k rows in the asymmetric detector and k=p, p represents thepitch, a(n) represents the weight of subset n and the value of a(n)should guarantee that

${{\sum\limits_{n = 0}^{N - k}{\alpha(n)}} = 1},$for example,

${{a(n)} = \frac{1}{N - k + 1}},$w_(n)(γ,β,i) represents, in subset n, the weight of the projection dataat the position of fan angle γ in the i^(th) row of the asymmetricdetector under the view angle β. The N rows of data are divided intoN−k+1 subsets here, i.e. the first to the k^(th) rows are subset 0; thesecond to the (k+1)^(th) rows are subset 1; . . . ; the (N−k)^(th) tothe (N−1)^(th) rows are subset N−k−1; and the (N−k+1)^(th) to the N^(th)rows are subset N−k. k rows of data are used in each subset.

For Region 3 and Region 1:

${w_{n}( {\gamma,\beta,i} )} = \{ \begin{matrix}{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {\beta - {\theta_{n,{m -}}( {\gamma,\beta,i} )}} )}{{\theta_{n,m}( {\gamma,\beta,i} )} - {\theta_{n,{m -}}( {\gamma,\beta,i} )}}},} & {{\theta_{n,{m -}}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,m}( {\gamma,\beta,i} )}} \\{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {{\theta_{n,{m +}}( {\gamma,\beta,i} )} - \beta} )}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} - {\theta_{n,m}( {\gamma,\beta,i} )}}},} & {{\theta_{n,m}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,{m +}}( {\gamma,\beta,i} )}} \\{0,} & {{otherwise},}\end{matrix} $wherein, M represents that there are M kinds of interpolation, eachcorresponding to a slope δ_(m) in a different reconstructed region;λ_(n,m) represents the weight in the n^(th) subset with the m^(th) kindof interpolation, and the value of λ_(n,m) should meet

${{\sum\limits_{m = 1}^{M}\lambda_{n,m}} = 1},$e.g.

${\lambda_{n,m} = \frac{1}{M}};{\theta_{n,m}( {\gamma,\beta,i} )}$represents the center of view angle when calculating the weightw_(n)(γ,β,i) in the n^(th) subset under the m^(th) kind ofinterpolation, and the weight thereof is 1; θ_(n,m−)(γ,β,i) representsthe lower boundary of the view angle when calculating w_(n)(γ,β,i) underthe m^(th) kind of interpolation, and the weight thereof is 0; andθ_(n.m+)(γ,β,i) represents the upper boundary of the view angle whencalculating w_(n)(γ,β,i) under the m^(th) kind of interpolation, and theweight thereof is 0.

For Region 3:

${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {\phi_{i,m} - \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {\phi_{i,m} + \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,m}( {\gamma,\beta,i} )} = {\phi_{i,m} - {\delta_{m}*\gamma}}}$wherein,

${\phi_{i,m} = \frac{2i\;\pi}{p}},$φ_(i,m) represents the center of view angle of the central channel inthe i^(th) row; and δ_(m) is the inclined slope of the m^(th) kind ofinterpolation.

For Region 1:

$\begin{matrix}{{\theta_{n,m}( {\gamma,\beta,i} )} = {\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )}} \\{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )}}}\end{matrix}$ $\begin{matrix}{{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} - \frac{2\;\pi}{p}}} \\{{= {\theta_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} - \frac{2\;\pi}{p}}},}\end{matrix}$ $\begin{matrix}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} + \frac{2\;\pi}{p}}} \\{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} + \frac{2\;\pi}{p}}}\end{matrix}$wherein γ₀ represents the largest fan angle at the small fan angle side;andΔγ represents the width of the transition region.

For Region 2:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{- \gamma_{0}},\beta,i} )} + {( {{w_{n}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} - {w_{n}( {{- \gamma_{0}},\beta,i} )}} )*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}}}$wherein,

${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{{trans}( {\gamma,a,b} )} = {f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )}},{{{and}\mspace{14mu}{f(x)}} = {{3*x^{2}} - {2*x^{3}}}}$

For Region 4:

${{w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{\gamma_{0} - {\Delta\gamma}},{\beta + {2*( {\gamma - \gamma_{0} + {\Delta\gamma}} )}},i} )}*( {1 - {{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}} )}},\mspace{79mu}{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}$is the transition function. Suppose Δγ=b and

${{\gamma_{0} - \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function and when its independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1, for example, a differentiable functionƒ(x)=3*x²−2*x³.

The process of performing image reconstruction using the method forimage reconstruction described herein under a helical scan is describedbelow using a detector of 16 rows as an example.

Suppose that the pitch of the helical scan is 9.

As shown in FIG. 5, the horizontal coordinate represents the rows of thedetector and the vertical coordinate represents the view angle β, and inthe horizontal coordinate direction, each row includes a plurality ofchannels (e.g. 888 channels). FIG. 5 is cited from U.S. Pat. No.6,873,676.

In this example, data of 16 rows are divided into 8 subsets, eachincluding data of 9 rows. The weight of each subset is α(n), Σα(n)=1.

Likewise, the projection data of the detector of 16 rows are alsodivided into five regions, as shown in FIG. 2. The reconstructed area isdepicted by the thick line in FIG. 6 in the sinusoidal space of theprojection data. FIG. 6 depicts the positions of the view angles whenthe reconstructed area corresponds to various channels in a certain rowof the detector. In Region 3, the reconstructed area is a slope linewhose slope is δ_(m) so as to apply the generalized helicalinterpolation algorithm. In Region 1 and Region 2, the reconstructedarea is a horizontal line that maintains the view angle value at therightmost end of the reconstructed area in Region 3. In Region 4, thereconstructed area is a slope line whose slope is 2. This helps toreduce the deviation of the reconstructed image slice from thecross-section in the axial direction, and it would be more meaningful tolimit the span of the reconstructed area of Regions 1 and 2 in the axialdirection, because the larger the span of the reconstructed area in theview angle direction is, the larger the span of the reconstructed areain the axial direction is. As a result, the greater the deviation of thereconstructed image slice from the cross-section is. Meanwhile, Regions1 and 2 have greater weights. The weight of Region 5 is 0, and theweight in Region 4 also gradually becomes 0.

After dividing the projection data into five regions, the view angleweighting is performed. The weights of Region 5 are 0, and the weightsof the remaining four regions are calculated as follows.

For Regions 3 and 1, the formula below is used:

${w_{n}( {\gamma,\beta,i} )} = \{ \begin{matrix}{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {\beta - {\theta_{n,{m -}}( {\gamma,\beta,i} )}} )}{{\theta_{n,m}( {\gamma,\beta,i} )} - {\theta_{n,{m -}}( {\gamma,\beta,i} )}}},} & {{\theta_{n,{m -}}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,m}( {\gamma,\beta,i} )}} \\{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {{\theta_{n,{m +}}( {\gamma,\beta,i} )} - \beta} )}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} - {\theta_{n,m}( {\gamma,\beta,i} )}}},} & {{\theta_{n,m}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,{m +}}( {\gamma,\beta,i} )}} \\{0,} & {{otherwise},.}\end{matrix} $

For Region 3, the weights in the subset are calculated by thegeneralized helical interpolation algorithm, and interpolation isperformed between conjugate projections.

${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {\phi_{i,m} - \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {\phi_{i,m} + \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,m}( {\gamma,\beta,i} )} = {\phi_{i,m} - {\delta_{m}*\gamma}}}$wherein,

${\phi_{i,m} = \frac{2i\;\pi}{p}},$φ_(i,m) represents the center of the view angle of the central channelin the i^(th) row; and δ_(m) is the inclined slope of the m^(th) kind ofinterpolation (see U.S. Pat. No. 6,873,676).

For Region 1, interpolation between rows is used for the weights in thesubset:

     θ_(n, m)(γ, β, i) = θ_(n, m)(−γ₀ + Δγ, β, i) = ϕ_(i, m) − δ_(m) * (−γ₀ + Δγ)${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {{{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} - \frac{2\pi}{p}} = {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\gamma}} )} - \frac{2\pi}{p}}}},{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {{{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} + \frac{2\pi}{p}} = {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\gamma}} )} + {\frac{2\pi}{p}.}}}}$wherein γ₀ represents the largest fan angle at the small fan angle side;and Δγ represents the width of the transition region.

The center of view angle of the interpolation function in Region 1 isjust the center of a view angle of the corresponding interpolationfunction in the end of Region 3 that is close to Region 1.

For Region 2, the interpolation transits from the interpolation betweenrows in Region 1 to the conjugate interpolation of Region 3 along ahorizontal direction:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{- \gamma_{0}},\beta,i} )} + {( {{w_{n}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} - {w_{n}( {{- \gamma_{0}},\beta,i} )}} )*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}}}$wherein,

${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{{trans}( {\gamma,a,b} )} = {f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )}},{{{and}\mspace{14mu}{f(x)}} = {{3*x^{2}} - {2*x^{3}}}}$wherein w_(n)(−γ₀,β,i) can be calculated from the weight formula ofRegion 1; andw_(n)(−γ₀+Δγ,β,i) can be calculated from the weight formula of Region 3.

For Region 4, the interpolation transits from the conjugateinterpolation of Region 3 to the 0 contribution of Region 5 along thedirection of the declined line shown in FIG. 6:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{\gamma_{0} - {\Delta\gamma}},{\beta + {2*( {\gamma - \gamma_{0} + {\Delta\gamma}} )}},i} )}*( {1 - {{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}} )}$wherein w_(n)(γ₀−Δγ,β+2*(γ−γ₀+Δγ),i) can be calculated from the weightformula of Region 3.

The finally obtained weights of projection data are as shown in FIG. 7.In FIG. 7, there are 16 blocks in the column direction, each blockrepresenting one row, and in each block, the column direction is thechannel (fan angle) direction, while the vertical direction is the viewangle direction.

Then, the projection data are weighted according to the obtainedweights. Finally, the tomographic image of the irradiated subject isreconstructed according to the weighted projection data.

As shown in FIG. 8, the leftmost part is the image reconstructed fromthe projection data obtained by the symmetric detector, the middle partis the image reconstructed from the projection data obtained by theasymmetric detector of this example by using the method for imagereconstruction described herein, and the rightmost part is the image ofthe difference image of the two images. The left two images have awindow width of 200 and a window level of 20; and the rightmost imagehas a window width of 50 and a window level of 0. The centers of allimages are in the center of scan. In this example, there are 888channels in the symmetrical condition, while the asymmetric detector has444 channels in the left and 362 channels in the right.

As can be seen from FIG. 8, the image (the middle image) reconstructedby the method for image reconstruction described above has almost thesame quality in the central region as the image reconstructed by thesymmetric detector.

According to another aspect, an apparatus for image reconstruction isprovided, which is used for image reconstruction according to theprojection data obtained by the asymmetric detector. The apparatusincludes a region dividing unit configured to divide the projection datainto five regions: region 1, region 2, region 3, region 4 and region 5,wherein Region 1 is an asymmetric region where there are detectingchannels but no detecting channels symmetrical about the centralchannel, Region 2 is a transition region where there are detectingchannels, and there are also detecting channels symmetrical about thecentral channel, Region 3 is a symmetric region where there aredetecting channels, and there are also detecting channels symmetricalabout the central channel, Region 4 is a transition region where thereare detecting channels, and there are also detecting channelssymmetrical about the central channel, and Region 5 is a truncatedregion where there are no detecting channels. The apparatus furtherincludes a view angle weighting unit configured to perform view angleweightings on the projection data in each of the five regionsand areconstructing unit configured to reconstruct the tomographic image ofthe irradiated subject from the weighted projection data.

For an axial scan, the weights of the projection data in the fiveregions are as follows: the weights of projection data in Region 1 are1; the weights of projection data in Region 3 are ½; the weights ofprojection data in Region 5 are 0; the weights of projection data inRegion 2 are 1˜½; and the weights of projection data in Region 4 are½˜0.

The weights of projection data in Region 2 are obtained from thefollowing formula:

${w(\gamma)} = {1 - {\frac{1}{2}*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}}}$wherein, w(γ) represents the weight of projection data obtained when thefan angle is γ; γ₀ represents the largest fan angle at the small fanangle side; Δγ represents the width of the transition region;

${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function, and when ƒ(x)'s independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

The weights of the projection data in Region 4 are obtained from thefollowing formula:

${w(\gamma)} = {\frac{1}{2} - {\frac{1}{2}*{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}}}$${trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is the transition function. Suppose Δγ=b and

${{\gamma_{0} - \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein, ƒ(x) is a differentiable function, and when ƒ(x)'s independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

For a helical scan, the weights of the projection data in the fiveregions are as follows: the weights of the projection data in Region 5are 0; and the weights of the projection data in the remaining fourregions are:

${\xi( {\gamma,\beta,i} )} = {\sum\limits_{n = 0}^{N - k}\;{{\alpha(n)}{w_{n}( {\gamma,\beta,i} )}}}$wherein, ξ(γ,β,i) represents the weight of the projection data at theposition of fan angle γ in the i^(th) row of the asymmetric detectorunder the view angle β;N represents the number of rows of the asymmetric detector, k representsconsecutive k rows in the asymmetric detector and k=p, p represents thepitch, a(n) represents the weight of subset n and Σa(n)=1, w_(n)(γ,β,i)represents, in subset n, the weight of the projection data at theposition of fan angle γ in the i^(th) row of the asymmetric detectorunder the view angle β.

For Region 3 and Region 1:

${w_{n}( {\gamma,\beta,i} )} = \{ \begin{matrix}{{\sum\limits_{m = 1}^{M}\;\frac{\lambda_{n,m}*( {\beta - {\theta_{n,{m -}}( {\gamma,\beta,i} )}} )}{{\theta_{n,m}( {\gamma,\beta,i} )} - {\theta_{n,{m -}}( {\gamma,\beta,i} )}}},} & {{\theta_{n,{m -}}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,m}( {\gamma,\beta,i} )}} \\{{\sum\limits_{m = 1}^{M}\;\frac{\lambda_{n,m}*( {{\theta_{n,{m +}}( {\gamma,\beta,i} )} - \beta} )}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} - {\theta_{n,m}( {\gamma,\beta,i} )}}},} & {{\theta_{n,m}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,{m +}}( {\gamma,\beta,i} )}} \\{0,} & {{otherwise},}\end{matrix} $wherein, λ_(n,m) represents the weight of the m^(th) kind ofinterpolation in the n^(th) subset; θ_(n.m)(γ,β,i) represents the centerof view angle when calculating the weight w_(n)(γ,β,i) in the n^(th)subset under the m^(th) kind of interpolation, and the weight thereof is1; θ_(n,m−)(γ,β,i) represents the lower boundary of the view angle whencalculating w_(n)(γ,β,i) under the m^(th) kind of interpolation, and theweight thereof is 0; and θ_(n.m+)(γ,β,i) represents the upper boundaryof the view angle when calculating w_(n)(γ,β,i) under the m^(th) kind ofinterpolation, and the weight thereof is 0.

For Region 3:

${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {\phi_{i,m} - \frac{\pi}{p} - {( {2 - \delta_{m}} )\gamma}}},{and}$${\theta_{n,{m +}}( {\gamma,\beta,i} )} = {\phi_{i,m} + \frac{\pi}{p} - {( {2 - \delta_{m}} )\gamma}}$θ_(n, m)(γ, β, i) = ϕ_(i, m) − δ_(m) * γwherein,

${\phi_{i,m} = \frac{2i\;\pi}{p}},$φ_(i,m) represents the center of view angle of the central channel inthe i^(th) row; and δ_(m) in is the inclined slope of the m^(th) kind ofinterpolation.

For Region 1:

θ_(n, m)(γ, β, i) = θ_(n, m)(−γ₀ + Δ γ, β, i) = ϕ_(i, m) − δ_(m) * (−γ₀ + Δ γ)${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {{{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} - \frac{2\pi}{p}} = {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\gamma}} )} - \frac{2\pi}{p}}}},{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {{{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} + \frac{2\pi}{p}} = {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\gamma}} )} + \frac{2\pi}{p}}}}$wherein γ₀ represents the largest fan angle at the small fan angle side;and Δγ represents the width of the transition region.

For Region 2:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{- \gamma_{0}},\beta,i} )} + {( {{w_{n}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} - {w_{n}( {{- \gamma_{0}},\beta,i} )}} )*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}}}$     wherein${\mspace{76mu}\;}{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}$is the transition function. Suppose Δγ=b and

${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$then,

${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$wherein ƒ(x) is a differentiable function and when ƒ(x)'s independentvariable varies from 0 to 1, the function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.

For Region 4:

${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{\gamma_{0} - {\Delta\gamma}},{\beta + {2*( {\gamma - \gamma_{0} + {\Delta\gamma}} )}},i} )}*{( {1 - {{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}} ).}}$

The technical solution of the apparatus for image reconstructiondescribed herein corresponds to the method for image reconstructiondescribed herein, so it will not be described in detail any more herein.

According to another aspect, a CT system is provided, which includes theapparatus for image reconstruction described herein.

While the specific embodiments of the present invention have beendescribed in conjunction with the drawings, those skilled in the art canmake many alternatives, modifications and equivalent substitution to thepresent invention without departing from the principle and spirit of thepresent invention, so such alternatives, modifications and equivalentsubstitution are intended to fall within the spirit and scope defined bythe appended claims.

What is claimed is:
 1. A method for image reconstruction according toprojection data obtained by an asymmetric detector, said methodcomprises: dividing the projection data into Region 1, Region 2, Region3, Region 4 and Region 5, Region 1 being an asymmetric region wherethere are detecting channels but no detecting channels symmetrical abouta central channel, Region 2 being a transition region where there aredetecting channels and there are also detecting channels symmetricalabout the central channel, Region 3 being a symmetric region where thereare detecting channels and there are also detecting channels symmetricalabout the central channel, Region 4 being a transition region wherethere are detecting channels and there are also detecting channelssymmetrical about the central channel, and Region 5 being a truncatedregion where there is no detecting channel; performing a view angleweighting on projection data in each of Region 1, Region 2, Region 3,Region 4, and Region 5, wherein for an axial scan, said performing aview angle weighting further comprises weighting the projection data inthe Regions such that weights of the projection data in Region 1 are 1,weights of the projection data in Region 3 are ½, weights of theprojection data in Region 5 are 0, weights of the projection data inRegion 2 are 1˜½, and weights of the projection data in Region 4 are½˜0; and reconstructing a tomographic image of an irradiated subjectfrom the weighted projection data.
 2. The method for imagereconstruction according to claim 1 further comprising obtaining theweights of the projection data in Region 2 from:${w(\gamma)} = {1 - {\frac{1}{2}*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}}}$wherein, w(γ) represents a weight of projection data obtained when a fanangle is γ, γ₀ represents a largest fan angle at a small fan angle side,Δγ represents a width of the transition region,${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is a transition function, and supposing Δγ=b and${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$ then${{{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}},$wherein ƒ(x) is a differentiable function, and when an independentvariable of ƒ(x) varies from 0 to 1, a function value varies from 0 to 1and satisfies ƒ(x)+ƒ(1−x)=1.
 3. The method for image reconstructionaccording to claim 2, further comprising obtaining the weights of theprojection data in Region 4 from:${{w(\gamma)} = {\frac{1}{2} - {\frac{1}{2}*{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}}}},{wherein}$${trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )$is the transition function, and supposing Δγ=b and${{\gamma_{0} - \frac{\Delta\gamma}{2}} = a},$ then${{{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}},$wherein ƒ(x) is a differentiable function, and when an independentvariable of ƒ(x) varies from 0 to 1, a function value varies from 0 to 1and satisfies ƒ(x)+ƒ(1−x)=1.
 4. The method for image reconstructionaccording to claim 1, wherein for a helical scan, said performing a viewangle weighting further comprising weighting the projection data in theRegions such that weights of the projection data in Region 5 are 0 andweights of the projection data in Region 1, Region 2, Region 3, andRegion 4 are:${\xi( {\gamma,\beta,i} )} = {\sum\limits_{n = 0}^{N - k}{{\alpha(n)}{w_{n}( {\gamma,\beta,i} )}}}$wherein ξ(γ,β, i) represents a weight of the projection data at aposition of a fan angle γ in an i^(th) row of an asymmetric detectorunder a view angle β, N represents a number of rows of the asymmetricdetector, k represents consecutive k rows in the asymmetric detector andk=p, p represents the pitch, a(n) represents a weight of a subset n andΣa(n)=1, w_(n)(γ,βi) represents a weight of the projection data at aposition of the fan angle γ in the i^(th) row of the asymmetric detectorunder the view angle β in the subset n.
 5. The method for imagereconstruction according to claim 4, wherein for Region 3 and Region 1:${w_{n}( {\gamma,\beta,i} )} = \{ \begin{matrix}{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {\beta - {\theta_{n,{m -}}( {\gamma,\beta,i} )}} )}{{\theta_{n,m}( {\gamma,\beta,i} )} - {\theta_{n,{m -}}( {\gamma,\beta,i} )}}},} & {{\theta_{n,{m -}}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,m}( {\gamma,\beta,i} )}} \\{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {{\theta_{n,{m +}}( {\gamma,\beta,i} )} - \beta} )}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} - {\theta_{n,m}( {\gamma,\beta,i} )}}},} & {{{\theta_{n,m}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,{m +}}( {\gamma,\beta,i} )}},} \\{0,} & {otherwise}\end{matrix} $ wherein λ_(n,m) represents a weight in an n^(th)subset with an m^(th) kind of interpolation, θ_(n,m)(γ,β,i) represents acenter of a view angle when calculating a weight w_(n)(γ,β,i) in then^(th) subset under the m^(th) kind of interpolation and a weightthereof is 1, θ_(n,m−)(γ,β,i) represents a lower boundary of the viewangle when calculating the weight w_(n)(γ,β,i) under the m^(th) kind ofinterpolation and a weight thereof is 0, and θ_(n,m+)(γ,β,i) representsan upper boundary of the view angle when calculating the weightw_(n)(γ,β,i) under the m^(th) kind of interpolation and a weight thereofis
 0. 6. The method for image reconstruction according to claim 5,wherein for Region 3:${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {\phi_{i,m} - \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {\phi_{i,m} + \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,m}( {\gamma,\beta,i} )} = {\phi_{i,m} - {\delta_{m}*\gamma}}}$${{wherein}\mspace{14mu}\phi_{i,m}\frac{2i\;\pi}{p}},$ φ_(i,m)represents a center of a view angle of the central channel in the i^(th)row, and δ_(m) is an inclined slope of the m^(th) kind of interpolation.7. The method for image reconstruction according to claim 6, wherein forRegion 1:     θ_(n, m)(γ, β, i) = θ_(n, m)(−γ₀ + Δγ, β, i) = ϕ_(i, m) − δ_(m) * (−γ₀ + Δγ)${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {{{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} - \frac{2\pi}{p}} = {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\gamma}} )} - \frac{2\pi}{p}}}},{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {{{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} + \frac{2\pi}{p}} = {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\gamma}} )} + \frac{2\pi}{p}}}}$wherein γ₀ represents a largest fan angle at small fan angle side, andΔγ represents a width of the transition region.
 8. The method for imagereconstruction according to claim 7, wherein for Region 2:${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{- \gamma_{0}},\beta,i} )} + {( {{w_{n}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} - {w_{n}( {{- \gamma_{0}},\beta,i} )}} )*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}$$\mspace{20mu}{{wherein}\mspace{14mu}{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}$is a transition function, and supposing Δγ=b and${{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}} = a},$ then${{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}$where ƒ(x) is a differentiable function and when an independent variableof ƒ(x) varies from 0 to 1, a function value varies from 0 to 1 andsatisfies ƒ(x)+ƒ(1−x)=1.
 9. The method for image reconstructionaccording to claim 8, wherein for Region 4:${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{\gamma_{0} - {\Delta\;\gamma}},{\beta + {2*( {\gamma - \gamma_{0} + {\Delta\;\gamma}} )}},i} )}*{( {1 - {{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}} ).}}$10. An apparatus for image reconstruction used for image reconstructionaccording to projection data obtained by an asymmetric detector, saidapparatus comprises: a region dividing unit configured to divide theprojection data into Region 1, Region 2, Region 3, Region 4 and Region5, Region 1 being an asymmetric region where there are detectingchannels but no detecting channels symmetrical about a central channel,Region 2 being a transition region where there are detecting channelsand there are also detecting channels symmetrical about the centralchannel, Region 3 being a symmetric region where there are detectingchannels and there are also detecting channels symmetrical about thecentral channel, Region 4 being a transition region where there aredetecting channels and there are also detecting channels symmetricalabout the central channel, and Region 5 being a truncated region wherethere is no detecting channel; a view angle weighting unit configured toperform view angle weighting on the projection data in each of Region 1,Region 2, Region 3, Region 4, and Region 5, wherein for an axial scan,weights of the projection data in the Regions are such that weights ofthe Projection data in Region 1 are 1, weights of the projection data inRegion 3 are ½, weights of the projection data in Region 5 are 0,weights of the projection data in Region 2 are 1˜½, and weights of theprojection data in Region 4 are ½˜0; and a reconstructing unitconfigured to reconstruct a tomographic image of an irradiated subjectfrom the weighted projection data.
 11. The apparatus for imagereconstruction according to claim 10, wherein the weights of theprojection data in Region 2 are obtained from:${w(\gamma)} = {1 - {\frac{1}{2}*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}$wherein, w(γ) represents a weight of projection data obtained when a fanangle is γ, γ₀ represents a largest fan angle at a small fan angle side,Δγ represents a width of the transition region,${trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )$is a transition function, and supposing Δγ=b and${{{- \gamma_{0}} + \frac{\Delta\;\gamma}{2}} = a},$ then${{{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}},$wherein ƒ(x) is a differentiable function, and when an independentvariable of ƒ(x) varies from 0 to 1, a function value varies from 0 to 1and satisfies ƒ(x)+ƒ(1−x)=1.
 12. The apparatus for image reconstructionaccording to claim 11, wherein the weights of the projection data inRegion 4 are obtained from:${{w(\gamma)} = {\frac{1}{2} - {\frac{1}{2}*{{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}}},{{wherein}\mspace{14mu}{{trans}( {\gamma,{{- \gamma_{0}} - \frac{\Delta\;\gamma}{2}},{\Delta\;\gamma}} )}}$is the transition function, and supposing Δγ=b and${{\gamma_{0} - \frac{\Delta\;\gamma}{2}} = a},$ then${{{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}},$wherein ƒ(x) is a differentiable function, and when an independentvariable of ƒ(x) varies from 0 to 1, a function value varies from 0 to 1and satisfies ƒ(x)+ƒ(1−x)=1.
 13. The apparatus for image reconstructionaccording to claim 10, wherein for a helical scan, weights of theprojection data in the Regions are such that weights of the projectiondata in Region 5 are 0 and weights of the projection data in Region 1,Region 2, Region 3, and Region 4 are:${\xi( {\gamma,\beta,i} )} = {\sum\limits_{n = 0}^{N - k}{{\alpha(n)}{w_{n}( {\gamma,\beta,i} )}}}$wherein ξ(γ,β,i) represents a weight of the projection data at aposition of a fan angle γ in an i^(th) row of an asymmetric detectorunder a view angle β, N represents a number of rows of the asymmetricdetector, k represents consecutive k rows in the asymmetric detector andk=p, p represents the pitch, a(n) represents a weight of a subset n andΣa(n)=1, w_(n)(γ,β,i) represents a weight of the projection data at aposition of the fan angle γ in the i^(th) row of the asymmetric detectorunder the view angle β in the subset n.
 14. The apparatus for imagereconstruction according to claim 13, wherein for Region 3 and Region 1:${w_{n}( {\gamma,\beta,i} )} = \{ \begin{matrix}{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {\beta - {\theta_{n,{m -}}( {\gamma,\beta,i} )}} )}{{\theta_{n,m}( {\gamma,\beta,i} )} - {\theta_{n,{m -}}( {\gamma,\beta,i} )}}},} & {{\theta_{n,{m -}}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,m}( {\gamma,\beta,i} )}} \\{{\sum\limits_{m = 1}^{M}\frac{\lambda_{n,m}*( {{\theta_{n,{m +}}( {\gamma,\beta,i} )} - \beta} )}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} - {\theta_{n,m}( {\gamma,\beta,i} )}}},} & {{{\theta_{n,m}( {\gamma,\beta,i} )} \leq \beta < {\theta_{n,{m +}}( {\gamma,\beta,i} )}},} \\{0,} & {otherwise}\end{matrix} $ wherein λ_(n,m) represents a weight in an n^(th)subset with an m^(th) kind of interpolation, θ_(n,m)(γ,β,i) represents acenter of a view angle when calculating a weight w_(n)(γ,β,i) in then^(th) subset under the m^(th) kind of interpolation and a weightthereof is 1, θ_(n,m−)(γ,β,i) represents a lower boundary of the viewangle when calculating the weight w_(n)(γ,β,i) under the m^(th) kind ofinterpolation and a weight thereof is 0, and θ_(n,m+)(γ,β,i) representsan upper boundary of the view angle when calculating the weightw_(n)(γ,β,i) under the m^(th) kind of interpolation and a weight thereofis
 0. 15. The apparatus for image reconstruction according to claim 14,wherein for Region 3:${{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {\phi_{i,m} - \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {\phi_{i,m} + \frac{\pi}{p} - {( {2 - \delta_{m}} )*\gamma}}},{{\theta_{n,m}( {\gamma,\beta,i} )} = {\phi_{i,m} - {\delta_{m}*\gamma}}}$${{{wherein}\mspace{14mu}\phi_{i,m}} = \frac{2\; i\;\pi}{p}},$ φ_(i,m)represents a center of a view angle of the central channel in the i^(th)row, and δ_(m) is an inclined slope of the m^(th) kind of interpolation.16. The apparatus for image reconstruction according to claim 15,wherein for Region 1: $\begin{matrix}{{\theta_{n,m}( {\gamma,\beta,i} )} = {\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )}} \\{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )}}}\end{matrix}$ $\begin{matrix}{{\theta_{n,{m -}}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} - \frac{2\pi}{p}}} \\{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} - \frac{2\pi}{p}}}\end{matrix}$ $\begin{matrix}{{\theta_{n,{m +}}( {\gamma,\beta,i} )} = {{\theta_{n,m}( {{{- \gamma_{0}} + {\Delta\;\gamma}},\beta,i} )} + \frac{2\pi}{p}}} \\{{= {\phi_{i,m} - {\delta_{m}*( {{- \gamma_{0}} + {\Delta\;\gamma}} )} + \frac{2\pi}{p}}},}\end{matrix}$ wherein γ₀ represents a largest fan angle at small fanangle side, and Δγ represents a width of the transition region.
 17. Theapparatus for image reconstruction according to claim 16, wherein forRegion 2:${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{- \gamma_{0}},\beta,i} )} + {( {{w_{n}( {{{- \gamma_{0}} + {\Delta\gamma}},\beta,i} )} -} )*{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\;\gamma}} )}}}$     wherein  $\mspace{79mu}{{trans}( {\gamma,{{- \gamma_{0}} + \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}$is a transition function, and supposing Δγ=b and${{{- \gamma_{0}} + \frac{\Delta\gamma}{2}} = a},$ then${{{trans}( {\gamma,a,b} )} = {{f( \frac{\gamma - ( {a - \frac{b}{2}} )}{b} )} = {f(x)}}},$wherein ƒ(x) is a differentiable function and when an independentvariable of ƒ(x) varies from 0 to 1, a function value varies from 0 to 1and satisfies ƒ(x)+ƒ(1−x)=1; and for Region 4:${w_{n}( {\gamma,\beta,i} )} = {{w_{n}( {{\gamma_{0} - {\Delta\gamma}},{\beta + {2*( {\gamma - \gamma_{0} + {\Delta\gamma}} )}},i} )}*{( {1 - {{trans}( {\gamma,{\gamma_{0} - \frac{\Delta\gamma}{2}},{\Delta\gamma}} )}} ).}}$18. A CT system for image reconstruction comprising: a tube configuredto emit X-rays toward an object; a detector system configured to convertX-rays received from said tube into projection data, said detectorsystem comprising at least one symmetric detector and at least oneasymmetric detector; and an apparatus used for image reconstructionaccording to the projection data obtained by the asymmetric detector,said apparatus comprises: a region dividing unit configured to dividethe projection data into Region 1, Region 2, Region 3, Region 4 andRegion 5, Region 1 being an asymmetric region where there are detectingchannels but no detecting channels symmetrical about a central channel,Region 2 being a transition region where there are detecting channelsand there are also detecting channels symmetrical about the centralchannel, Region 3 being a symmetric region where there are detectingchannels and there are also detecting channels symmetrical about thecentral channel, Region 4 being a transition region where there aredetecting channels and there are also detecting channels symmetricalabout the central channel, and Region 5 being a truncated region wherethere is no detecting channel; a view angle weighting unit configured toperform view angle weighting on the projection data in each of Region 1,Region 2, Region 3, Region 4, and Region 5, wherein for an axial scan,weights of the projection data in the Regions are such that weights ofthe projection data in Region 1 are 1, weights of the Projection data inRegion 3 are ½, weights of the projection data in Region 5 are 0,weights of the projection data in Region 2 are 1˜½, and weights of theprojection data in Region 4 are ½˜0; and a reconstructing unitconfigured to reconstruct a tomographic image of an irradiated subjectfrom the weighted projection data.